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The phrase "perfectly impossible" is correct and usable in written English.
You can use this phrase to emphasize that something is not possible at all. For example, "It is perfectly impossible to complete this task in such a short period of time."
Exact(1)
How perfectly impossible it is to grow a good lawn in India.
Similar(58)
Unfortunately, modeling an electorate perfectly is impossible, especially when an election is many months away.
He showed that the perfectly efficient engine was impossible even in principle.
And there, perfectly summarized, is the impossible, impenetrable conundrum of pain.
While I mourn the loss of Linda Bishop, society can't expect the mental-health system to do the impossible: predict perfectly, and save everyone.
Arsène Wenger, one of those greatly influenced by him, once said it would be impossible to perfectly replicate the Total Football of early 70s Ajax and Holland without Cruyff on the field.
The British historian Michael Howard noted that it was impossible to perfectly prepare military forces for the next war; what is important is to make sure that you have not gotten the preparations so wrong that the military cannot quickly adapt when it is next needed.
First, the presence of channel estimation errors or time variations makes it impossible to perfectly suppress interference [5, 6].
However, perfectly similar cases are impossible to find, and this study cannot claim to be exhaustive about similarities and differences.
However, it is impossible to perfectly classify the few reported attackers, since attacks employed different behaviors in reaction to the defensive strategies exhibited by the crowd.
Natural dimensional variations of the bamboo and tolerances in the knots, however, made it impossible to perfectly match each label everywhere as cumulative slippage occasionally built up (see Fig. 17).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com